New Foundations for Rewriting Logic

Abstract

This paper presents an abstract treatment of the foundations of rewriting logic, generalising in three ways: an arbitrary 2-category plays the role of the specific 2-category Cat; the foundations are rendered fully independent of the underlying equational logic; and the semantics covers non-conventional sentences. Despite the high level of abstraction a number of properties of interest to Computing Science are seen to hold including the existence of initial models, liberality along theory morphisms, exactness, and a completeness theorem for a very abstract notion of deduction.